The third seeded pair of Bhupathi and Canadian Daniel Nestor bowed out of the men's doubles with a 4-6 6-7 (4) defeat against Spaniard Feliciano Lopez and Milos Raonic of Canada.
Rohan Bopanna had also made a first round exit in the same event with American partner Rajeev Ram.
In the women's doubles, eighth seeded team of Sania and America's Bethanie Mattek-Sands went down fighting 7-6 (8) 3-6 6-10 against American Lisa Raymond and Samantha Stosur of Australia in their opening round clash.